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nI'veI've been struggling with the use of Grassmann numbers in QFT e.g. Peskin and Schroeder. They are introduced as "numbers" whose product is antisymmetric, and associative (this isn't said, but used in following calculations), furthermore, they can be multiplied by complex numbers in the usual way. This all means that they are a complex algebra that alternates and is associative. My problem is that this isn't enough to specify what they are and how they behave.

Example: The exterior algebra $$\Lambda \mathbb{C^2}$$ has the property that the product of any three elements must vanish. The exterior algebra $$\Lambda \mathbb{C^3}$$ does not have this property. Both satisfy the conditions for Grassmann numbers.

So, it seems to me that the Grassmann numbers described in field theory are underspecified. Have I got something confused? If not, how should they be accurately specified?

nI've been struggling with the use of Grassmann numbers in QFT e.g. Peskin and Schroeder. They are introduced as "numbers" whose product is antisymmetric, and associative (this isn't said, but used in following calculations), furthermore, they can be multiplied by complex numbers in the usual way. This all means that they are a complex algebra that alternates and is associative. My problem is that this isn't enough to specify what they are and how they behave.

Example: The exterior algebra $$\Lambda \mathbb{C^2}$$ has the property that the product of any three elements must vanish. The exterior algebra $$\Lambda \mathbb{C^3}$$ does not have this property. Both satisfy the conditions for Grassmann numbers.

So, it seems to me that the Grassmann numbers described in field theory are underspecified. Have I got something confused? If not, how should they be accurately specified?

I've been struggling with the use of Grassmann numbers in QFT e.g. Peskin and Schroeder. They are introduced as "numbers" whose product is antisymmetric, and associative (this isn't said, but used in following calculations), furthermore, they can be multiplied by complex numbers in the usual way. This all means that they are a complex algebra that alternates and is associative. My problem is that this isn't enough to specify what they are and how they behave.

Example: The exterior algebra $$\Lambda \mathbb{C^2}$$ has the property that the product of any three elements must vanish. The exterior algebra $$\Lambda \mathbb{C^3}$$ does not have this property. Both satisfy the conditions for Grassmann numbers.

So, it seems to me that the Grassmann numbers described in field theory are underspecified. Have I got something confused? If not, how should they be accurately specified?

2 added 4 characters in body; edited tags; edited title

# What are GrassmanGrassmann numbers in field theory?

I'venI've been struggling with the use of GrassmanGrassmann numbers in QFT e.g. Peskin and Schroeder. They are introduced as "numbers" whose product is antisymmetric, and associative (this isn't said, but used in following calculations), furthermore, they can be multiplied by complex numbers in the usual way. This all means that they are a complex algebra that alternates and is associative. My problem is that this isn't enough to specify what they are and how they behave.

Example: The exterior algebra $$\Lambda \mathbb{C^2}$$ has the property that the product of any three elements must vanish. The exterior algebra $$\Lambda \mathbb{C^3}$$ does not have this property. Both satisfy the conditions for GrassmanGrassmann numbers.

So, it seems to me that the GrassmanGrassmann numbers described in field theory are underspecified. Have I got something confused? If not, how should they be accurately specified?

# What are Grassman numbers in field theory?

I've been struggling with the use of Grassman numbers in QFT e.g. Peskin and Schroeder. They are introduced as "numbers" whose product is antisymmetric, and associative (this isn't said, but used in following calculations), furthermore, they can be multiplied by complex numbers in the usual way. This all means that they are a complex algebra that alternates and is associative. My problem is that this isn't enough to specify what they are and how they behave.

Example: The exterior algebra $$\Lambda \mathbb{C^2}$$ has the property that the product of any three elements must vanish. The exterior algebra $$\Lambda \mathbb{C^3}$$ does not have this property. Both satisfy the conditions for Grassman numbers.

So, it seems to me that the Grassman numbers described in field theory are underspecified. Have I got something confused? If not, how should they be accurately specified?

# What are Grassmann numbers in field theory?

nI've been struggling with the use of Grassmann numbers in QFT e.g. Peskin and Schroeder. They are introduced as "numbers" whose product is antisymmetric, and associative (this isn't said, but used in following calculations), furthermore, they can be multiplied by complex numbers in the usual way. This all means that they are a complex algebra that alternates and is associative. My problem is that this isn't enough to specify what they are and how they behave.

Example: The exterior algebra $$\Lambda \mathbb{C^2}$$ has the property that the product of any three elements must vanish. The exterior algebra $$\Lambda \mathbb{C^3}$$ does not have this property. Both satisfy the conditions for Grassmann numbers.

So, it seems to me that the Grassmann numbers described in field theory are underspecified. Have I got something confused? If not, how should they be accurately specified?

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# What are Grassman numbers in field theory?

I've been struggling with the use of Grassman numbers in QFT e.g. Peskin and Schroeder. They are introduced as "numbers" whose product is antisymmetric, and associative (this isn't said, but used in following calculations), furthermore, they can be multiplied by complex numbers in the usual way. This all means that they are a complex algebra that alternates and is associative. My problem is that this isn't enough to specify what they are and how they behave.

Example: The exterior algebra $$\Lambda \mathbb{C^2}$$ has the property that the product of any three elements must vanish. The exterior algebra $$\Lambda \mathbb{C^3}$$ does not have this property. Both satisfy the conditions for Grassman numbers.

So, it seems to me that the Grassman numbers described in field theory are underspecified. Have I got something confused? If not, how should they be accurately specified?